General parametric representation of real 2-D stable polynomials

The theory of multidimensional systems gained enormous importance in the last years. Similar to the one-dimensional case, stability of such systems plays a crucial role. In this context so called scattering Hurwitz polynomials (in the continuous case) and scattering Schur polynomials (in the discrete) case are in the focus of interest. In the present paper a parametric representation for real two-variable scattering Schur polynomials is given. The following features of this model makes it best suited for the computer based design of 2-D systems, namely no dependencies between the real valued parameters, coverage of the whole class of 2-D scattering Schur polynomials, and the coefficients of the polynomials are rational functions of the parameters. The synthesis of two-dimensional (2-D) lossless networks and Householder matrices form the basis of our considerations.